Homogeneous Besov Spaces in Dunkl setting

TL;DR

This paper characterizes homogeneous Besov spaces within the Dunkl setting using a novel discrete reproducing formula based on differences of the Dunkl-Poisson kernel, involving both Euclidean and Dunkl metrics.

Contribution

It introduces a new approach to defining Besov spaces in the Dunkl setting with a novel decomposition and test functions, expanding the analytical framework.

Findings

Established a new discrete reproducing formula for Dunkl-Besov spaces

Developed new test functions and distributions for Dunkl analysis

Provided a novel decomposition method for these function spaces

Abstract

The purpose of this paper is to characterize the homogeneous Besov space in the Dunkl setting. We utilize a new discrete reproducing formula, that is, the building blocks are differences of the Dunkl-Poisson kernel which involves both the Euclidean metric and the Dunkl metric. To introduce the Besov spaces in the Dunkl setting, new test functions and distributions are introduced, and a new decomposition is established.